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We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian…

We start a systematic study of the Lema\^{i}tre-Tolman-Bondi (LTB) model as applied to the large scale structure and its evolution. Here we study three possible initial conditions of the LTB models which are asymptotically FRW at large…

The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference…

We propose a lightweight deep convolutional neural network (lCNN) to estimate cosmological parameters from simulated three-dimensional dark matter (DM) halo distributions and associated statistics. The training dataset comprises 2000…

We have developed an image-based convolutional neural network (CNN) that is applicable for quantitative time-resolved measurements of the fragmentation behavior of opaque brittle materials using ultra-high speed optical imaging. This model…

While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not…

Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhibits a property of power-like decaying autocorrelation…

This work develops a comprehensive mathematical theory for a class of stochastic processes whose local regularity adapts dynamically in response to their own state. We first introduce and rigorously analyze a time-varying fractional…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. In many applications, the spatial distribution of a field needs to be…

The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact…

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…

Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains…

Eclipsing binaries provide one of the most direct mechanisms for measuring stellar properties such as mass and radius, but historically, determining these properties has been non-trivial and computationally prohibitive. As such, only a…

A common method for delineating urban and suburban boundaries is to identify clusters of spatial units that are highly interconnected in a network of commuting flows, each cluster signaling a cohesive economic submarket. It is critical that…

We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases. More specifically, we show that, for activations which are…

Binary neural networks (BNNs) have 1-bit weights and activations. Such networks are well suited for FPGAs, as their dominant computations are bitwise arithmetic and the memory requirement is also significantly reduced. However, compared to…

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…

Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics,…